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Paul Ruet

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

6 papers

2 author rows

TCS Journal 2024 Journal Article

From multivalued to Boolean functions: Preservation of soft nested canalization

Élisabeth Remy
Paul Ruet

Nested canalization (NC) is a property of Boolean functions which has been recently extended to multivalued functions. We study the effect of the Van Ham mapping (from multivalued to Boolean functions) on this property. We introduce the class of softly nested canalizing (SNC) multivalued functions, and prove that the Van Ham mapping sends SNC multivalued functions to NC Boolean functions. Since NC multivalued functions are SNC, this preservation property holds for NC multivalued functions as well. We also study the relevance of SNC functions in the context of gene regulatory network modelling.

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CSL Conference 2005 Conference Paper

Permutative Logic

Jean-Marc Andreoli
Gabriele Pulcini
Paul Ruet

Abstract Recent work establishes a direct link between the complexity of a linear logic proof in terms of the exchange rule and the topological complexity of its corresponding proof net, expressed as the minimal rank of the surfaces on which the proof net can be drawn without crossing edges. That surface is essentially computed by sequentialising the proof net into a sequent calculus which is derived from that of linear logic by attaching an appropriate structure to the sequents. We show here that this topological calculus can be given a better-behaved logical status, when viewed in the variety-presentation framework introduced by the first author. This change of viewpoint gives rise to permutative logic, which enjoys cut elimination and focussing properties and comes equipped with new modalities for the management of the exchange rule. Moreover, both cyclic and linear logic are shown to be embedded into permutative logic. It provides the natural logical framework in which to study and constrain the topological complexity of proofs, and hence the use of the exchange rule.

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I&C Journal 2003 Journal Article

Non-commutative logic III: focusing proofs

Roberto Maieli
Paul Ruet

It is now well-established that the so-called focalization property plays a central role in the design of programming languages based on proof search, and more generally in the proof theory of linear logic. We present here a sequent calculus for non-commutative logic (NL) which enjoys the focalization property. In the multiplicative case, we give a focalized sequentialization theorem, and in the general case, we show that our focalized sequent calculus is equivalent to the original one by studying the permutabilities of rules for NL and showing that all permutabilities of linear logic involved in focalization can be lifted to NL permutabilities. These results are based on a study of the partitions of partially ordered sets modulo entropy.

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I&C Journal 2001 Journal Article

Linear Concurrent Constraint Programming: Operational and Phase Semantics

François Fages
Paul Ruet
Sylvain Soliman

In this paper we give a logical semantics for the class CC of concurrent constraint programming languages and for its extension LCC based on linear constraint systems. Besides the characterization in intuitionistic logic of the stores of CC computations, we show that both the stores and the successes of LCC computations can be characterized in intuitionistic linear logic. We illustrate the usefulness of these results by showing with examples how the phase semantics of linear logic can be used to give simple “semantical” proofs of safety properties of LCC programs.

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CSL Conference 1998 Conference Paper

Concurrent Constraint Programming and Non-commutative Logic

Paul Ruet
François Fages

Abstract This paper presents a connection between the intuitionistic fragment of a non-commutative version of linear logic introduced by the first author (NLI) and concurrent constraint programming (CC). We refine existing logical characterizations of operational aspects of CC, by providing a logical interpretation of finer observable properties of CC programs, namely stores, successes and suspensions.

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TCS Journal 1997 Journal Article

Combining explicit negation and negation by failure via Belnap's logic

Paul Ruet
François Fages

This paper deals with logic programs containing two kinds of negation: negation as failure and explicit negation. This allows two different forms of reasoning in the presence of incomplete information. Such programs have been introduced by Gelfond and Lifschitz and called extended programs. We provide them with a logical semantics in the style of Kunen, based on Belnap's four-valued logic, and an answer sets' semantics that is shown to be equivalent to that of Gelfond and Lifschitz. The proofs rely on a translation into normal programs, and on a variant of Fitting's extension of logic programming to bilattices.

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